acf2msd

<p>Length-<code>N</code> autocorrelation vector of a stationary increment sequence.</p>

<p>Converts the autocorrelation of a stationary increment sequence <code>dx = (x_1 - x_0, ..., x_N - x_(N-1))</code> to the mean squared displacement (MSD) of the corresponding positions, i.e., <code>MSD_i = E[(x_i - x_0)^2]</code>.</p>

Likelihood evaluations for stationary Gaussian time series are typically obtained via the Durbin-Levinson algorithm, which scales as O(n^2) in the number of time series observations.  This package provides a "superfast" O(n log^2 n) algorithm written in C++, crossing over with Durbin-Levinson around n = 300.  Efficient implementations of the score and Hessian functions are also provided, leading to superfast versions of inference algorithms such as Newton-Raphson and Hamiltonian Monte Carlo.  The C++ code provides a Toeplitz matrix class packaged as a header-only library, to simplify low-level usage in other packages and outside of R.

Martin Lysy

SuperGauss

acf2msd: Convert autocorrelation of stationary increments to mean squared displacement of posititions.

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